Mathematics, 29.01.2021 16:20 u8p4

Suppose U is a set containing 75 elements and that A1, A2, A3 and A4 are subsets of U such that each subset Ai contains 28 elements, the intersection of any two of the four subsets contains 12 elements, the intersection of any three of the four subsets contains 5 elements, and the intersection of all four subsets contains 1 element.

a. What is |A1 ∪ A2 ∪ A3 ∪ A4|?
b. How many elements belong to exactly two of the four subsets?

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